Improvement Of The Piecewise Approximation Methods

Abstract

A piecewise approximation method is described for planar curves. The order of classical piecewise approximations is improved. The method exploits the freedom in the choice of the parametrization and rises the approximation order up to J0L where m S 6 3 ' is the degree of the approximating polynomial parametrization. For the case of m = 5, a quintic polynomial curve is constructed which approximates with order 8. Moreover, we show for a class of curves of non-zero measure that the optimal rate 2m is achieved.